What is the value of $a$ if the lines $2y - 2a = 6x$ and $y + 1 = (a + 6)x$ are parallel?
Putting the first equation in slope-intercept form gives $y = 3x + a$ which means this line has a slope of 3.  Similarly the second equation gives $y = (a + 6)x - 1,$ meaning it has a slope of $a + 6$.  Since the two lines are parallel they have equal slopes: $3 = a + 6 \Rightarrow a = \boxed{-3}$.